A particle of mass 2 kg moves along the x-axis under the influence of a force given by F = 10 - 2x Newtons. If the particle starts from rest at x = 0, what is its speed at x = 5 meters?

B. 0 m/s — The work done by the force is equal to the change in kinetic energy. Integrating the force from 0 to 5 gives zero work, implying the final kinetic energy is zero.

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$A particle of mass m = 2 kg moves along the x -axis under the influence of a force given by F = 10 - 2 x N . If the particle starts from rest at x = 0, what is its speed at x = 5 m ?$

A. $5 m/s$
B. $0 m/s$
C. $10 m/s$
D. $2.5 m/s$

Show correct answer & step-by-step solution

Correct answer: B — $0 m/s$

Solution

The work done is W = \int_{0}^{5} (10 - 2 x) d x = [10 x - x^{2}]_{0}^{5} = 50 - 25 = 25 J . Wait, the calculation shows W = 25 J, so 0.5 \times 2 \times v^{2} = 25, leading to v = 5 m/s .

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A particle of mass m=2 kg moves along the x-axis under the influence of a force given by F=10−2x N. If the particle starts from rest at x=0, what is its speed at x=5 m?

Solution

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More Work Energy Power practice questions

$A particle of mass m = 2 kg moves along the x -axis under the influence of a force given by F = 10 - 2 x N . If the particle starts from rest at x = 0, what is its speed at x = 5 m ?$